Building blocks designed to be placed side-by-side in courses and having connectors on their upper and lower sides for attaching blocks in adjacent courses together, are known in the art. For example, in the toy building block art, LEGO (trademark) blocks have mating posts and recesses on their top and bottom sides respectively for attachment of blocks in vertically adjacent courses, as shown in U.S. Pat. No. 3,005,282 Christiansen. Since such blocks do not have any side connecting means, it is not possible to attach them side-by-side in a single layer, in order to create a span, for example to construct a horizontal roof or beam. Blocks having side connecting means are known, but they are adapted only to attach blocks horizontally that are also connected vertically, and are not adapted to construct weight-bearing horizontal structures.